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  • Calculus AB is designed to be taught over a full high school academic year. It is possible to spend some time on elementary functions and still cover the Calculus AB curriculum within a year. However, if students are to be adequately prepared for the Calculus AB examination, most of the year must be devoted to topics in differential and integral calculus. These topics are the focus of the AP Exam.


    Course Goals

    Students should be able to:

    • work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations.
    • understand the meaning of the derivative in terms of a rate of change and local linear approximation and they should be able to use derivatives to solve a variety of problems.
    • understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.
    • understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
    • communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.
    • model a written description of a physical situation with a function, a differential equation, or an integral.
    • use technology to help solve problems, experiment, interpret results, and verify conclusions.
    • determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
    • develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

    The topics covered in the course include:

    1. Functions, Graphs, and Limits
      • Analysis of Graphs
      • Limits of Functions (incl. one-sided limits)
      • Asymptotic and Unbounded Behavior
      • Continuity as a Property of Functions
    2. Derivatives
      • Concept of the Derivative
      • Derivative at a Point
      • Derivative as a Function
      • Second Derivatives
      • Applications of Derivatives
      • Computation of Derivatives
    3. Integrals
      • Interpretations and Properties of Definite Integrals
      • Applications of Integrals
      • Fundamental Theorem of Calculus
      • Techniques of Antidifferentiation
      • Applications of Antidifferentiation
      • Numerical Approximations to Definite Integrals

    For more detail on the course topics covered in Calculus AB, review the AP Calculus Course and Exam Description.

     

    Calculus BC can be offered by schools that are able to complete all the prerequisites before the course. Calculus BC is a full-year course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics. Both courses represent college-level mathematics for which most colleges grant advanced placement and credit. The content of Calculus BC is designed to qualify the student for placement and credit in a course that is one course beyond that granted for Calculus AB.

    Course Goals

    Students should be able to:

    • Work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations.
    • Understand the meaning of the derivative in terms of a rate of change and local linear approximation and they should be able to use derivatives to solve a variety of problems.
    • Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.
    • Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
    • Communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.
    • Model a written description of a physical situation with a function, a differential equation, or an integral.
    • Use technology to help solve problems, experiment, interpret results, and verify conclusions.
    • Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
    • Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

    The topic outline for Calculus BC includes all Calculus AB topics. Additional topics are marked with a plus sign (+) or an asterisk (*). The topics covered in the course include:

    1. Functions, Graphs, and Limits
      • Analysis of Graphs
      • Limits of Functions (incl. one-sided limits)
      • Asymptotic and Unbounded Behavior
      • Continuity as a Property of Functions
      • *Parametric, Polar, and Vector Functions
    2. Derivatives
      • Concept of the Derivative
      • Derivative at a Point
      • Derivative as a Function
      • Second Derivatives
      • Applications of Derivatives
      • Computation of Derivatives
    3. Integrals
      • Interpretations and Properties of Definite Integrals
      • *Applications of Integrals
      • Fundamental Theorem of Calculus
      • Techniques of Antidifferentiation
      • Applications of Antidifferentiation
      • Numerical Approximations to Definite Integrals
    4. *Polynomial Approximations and Series
      • *Concept of Series
      • *Series of constants
      • *Taylor Series

    For more detail on the course topics covered in Calculus BC, see the Course and Exam Description.